I need help in finding that in t years from now, one investment plan will be generating profit at the rate of
p1(t) = 130+t^2 thousand dollars per year.
While a second investment will be generating P2(t) = 273+2t thousand dollars per year.
a) For how many years does the rate of profitability of the second investment exceed that of the first?
I KNOW THE ANSWER FOR THIS IS 13
B) What is the net excess profit, in hundreds of dollars, assuming that you invest in the second plan for the time period determined in part a?
p1(t) = 130+t^2 thousand dollars per year.
While a second investment will be generating P2(t) = 273+2t thousand dollars per year.
a) For how many years does the rate of profitability of the second investment exceed that of the first?
I KNOW THE ANSWER FOR THIS IS 13
B) What is the net excess profit, in hundreds of dollars, assuming that you invest in the second plan for the time period determined in part a?
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First figure out where these intersect to figure out our region of integration.
t^2 + 130 = 2t + 273
t^2 - 2t - 143 = 0
(t - 13)(t + 11) = 0
t = 13
t = -11
But i am going to go on a whim and say that since we are only concerned with what we can invest at this moment our region of integration will be from 0 to 13
So for part A it will be 13 years
∫ (273 + 2t) - (130 + t^2) dt
273t + t^2 - 130t - (1/3)t^3 + C
143t + t^2 - (1/3)t^3 evaluate from 0 to 13
(143*13) + (13^2) - (1/3)(13^3) = 3887/3 which is approximately 1295.67. in hundreds of dollars we would round up to 13
t^2 + 130 = 2t + 273
t^2 - 2t - 143 = 0
(t - 13)(t + 11) = 0
t = 13
t = -11
But i am going to go on a whim and say that since we are only concerned with what we can invest at this moment our region of integration will be from 0 to 13
So for part A it will be 13 years
∫ (273 + 2t) - (130 + t^2) dt
273t + t^2 - 130t - (1/3)t^3 + C
143t + t^2 - (1/3)t^3 evaluate from 0 to 13
(143*13) + (13^2) - (1/3)(13^3) = 3887/3 which is approximately 1295.67. in hundreds of dollars we would round up to 13
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haha